Consider filling compressed argon from a high pressure supply line. Before filli

Question

Consider filling compressed argon from a high pressure supply line. Before filling, the cylinder contains 10 bar of argon at room temperature. The valve is then opened, exposing the tank 50 bar line at room temperature until the pressure of the cylinder reaches 50 bar. The valve is then closed. For argon take Cp=(5/2)R and the molecular weight to be 40 kg/kmole. You may use the ideal gas model

a) What is the temperature right after the valve is closed?

b) If the cylinder sits in storage for a long time, how much heat is transferred (in kJ/kg)?

c) What is the pressure of the cylinder when it is shipped (after it was stored for a long time)?

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what I have so far is h(hat) = u1(hat) + p(vhat)

u2 = m2 * u2(hat)

u1 = m1 * u1(hat)

and m2 - m1 = ( m2 * u2(hat) - m1 * u1(hat) ) / h(hat)

replacing mass to moles (n) and subbing the rest gets to

( p2 * v2 / RT2 ) - (p1 * v1 / RT1) = (P2 * v2 / RT2) * u2(hat) - ( p1 * v1 / RT1 ) * u1(hat)

and the right side divided by subbing h(hat)

not sure if where to head from there or even if I'm going in the right direction after all equation manipulations...

Explanation / Answer

T2=(P2*(Cp/Cv)*T1)/(P2-P1 + P1/T1*(Cp/Cv)*T1 I plugged in the given value for Cp used Cv=Cp-R used P2=50bar P1=10bar T1=298K and got 59.4 However I am pretty sure the temperature wouldn't go down, if anything it should go up since it is being compressed to a higher pressure. can anyone help maybe this equation is wrong or something? my prof writes really sloppy and I can't read it properly sometimes, let me know if this is the right forum too I wasn't sure where to put this question!

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